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Fundamental solutions and asymptotic numerical methods for bifurcation analysis of nonlinear bi‐harmonic problems

Abstract : New algorithms, combining asymptotic numerical method (ANM) and method of fundamental solutions, are proposed to compute bifurcation points on branch solutions of a nonlinear bi-harmonic problem. Three methods, mainly based on asymptotic developments framework, are then proposed. The first one consists in exploiting the ANM step accumulation close to the bifurcation points on a solution branch, the second method allows the introduction of an indicator that vanishes at the bifurcation points, and finally the first real root of the Padé approximant denominator represents the third bifurcation indicator. Two numerical examples are considered to analyze the robustness of these algorithms.
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https://hal.univ-lorraine.fr/hal-03240883
Contributor : Hamid Zahrouni <>
Submitted on : Friday, May 28, 2021 - 12:40:31 PM
Last modification on : Saturday, June 12, 2021 - 3:37:18 AM

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Abdeljalil Tri, Omar Askour, Bouazza Braikat, Hamid Zahrouni, Michel Potier‐ferry. Fundamental solutions and asymptotic numerical methods for bifurcation analysis of nonlinear bi‐harmonic problems. Numerical Methods for Partial Differential Equations, Wiley, 2019, 35 (6), pp.2091-2102. ⟨10.1002/num.22403⟩. ⟨hal-03240883⟩

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